I don't use CC. I save all my books to a folder on a NAS, using a connection to a folder as a device, from calibre. I do this whenever I update my books or add new books to my collection.
Then on my device I run an app, FolderSync, that automatically keeps a folder on my device synced to the folder on the NAS. The app only attempts to sync if I am charging my device, or if I request it.
Other options include various cloud services, if you don’t have a NAS that is on 24/7.
Currently I have around 3800 books, in slightly less than 10 GB, kept in sync this way. Since the app syncs, only new or changed books will transfer each sync, so it is typically very fast. If I make updates to many books I may send the whole library. That can take a while, but it's done while I charge my device while I am sleeping.
I still have to tell my reading app to update the bookshelf on the device.